Nonlinear PI control of uncertain systems: an alternative to parameter adaptation

R. Ortega, A. Astolfi, N. Barabanov
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引用次数: 60

Abstract

A novel approach to stabilization and trajectory tracking for nonlinear systems with unknown parameters and uncertain disturbances is developed. We take a drastic departure from the classical adaptive control approach consisting of a parameterized feedback law and an identifier, which tries to minimize a tracking (or prediction) error. Instead, we propose a simple nonlinear PI structure that generates a stable error equation with a perturbation function that exhibits at least one root. This root is made all attractive equilibrium by suitably adjusting the nonlinear PI gains. We consider the two basic problems of: (i) matched uncertainties, when the uncertain terms are in the image of the input matrix, and (ii) unknown control directions, when the control signal is multiplied by a gain of unknown sign.
不确定系统的非线性PI控制:参数自适应的替代方法
提出了一种具有未知参数和不确定扰动的非线性系统的镇定与轨迹跟踪新方法。我们与经典的自适应控制方法截然不同,该方法由参数化反馈律和标识符组成,试图将跟踪(或预测)误差最小化。相反,我们提出了一个简单的非线性PI结构,该结构产生一个稳定的误差方程,该方程具有至少一个根的扰动函数。通过适当调整非线性PI增益,使该根达到全吸引平衡。我们考虑两个基本问题:(i)匹配的不确定性,当不确定性项在输入矩阵的图像中;(ii)未知的控制方向,当控制信号乘以一个未知符号的增益。
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